Inhomogeneous Broadening of Photoluminescence Spectra and Kinetics of Nanometer-Thick (Phenethylammonium)2PbI4 Perovskite Thin Films: Implications for Optoelectronics

An outstanding potentiality of layered two-dimensional (2D) organic–inorganic hybrid perovskites (2DHPs) is in the development of solar cells, photodetectors, and light-emitting diodes. In 2DHPs, an exciton is localized in an atomically thin lead(II) halide inorganic layer of sub-nanometer thickness as in a quantum well sandwiched between organic layers as energetic and dielectric barriers. In previous years, versatile optical characterization of 2DHPs has been carried out mainly for thin flakes of single crystals and ultrathin (of the order of 20 nm) polycrystalline films, whereas there is a lack of optical characterization of thick (hundreds of nanometers) polycrystalline films, fundamentals for fabrication of devices. Here, with the use of photoluminescence (PL) and absorption spectroscopies, we studied the exciton behavior in ∼200 nm polycrystalline thin films of 2D perovskite (PEA)2PbI4, where PEA is phenethylammonium. Contrary to the case of ultrathin films, we have found that peak energies and line width of the excitonic bands in our films demonstrate unusual extremely weak sensitivity to temperature in 20–300 K diapason. The excitonic PL band is characterized by a significant (∼30 meV) Stokes shift with respect to the corresponding absorption band as well as by a full absence of the exciton fine structure at cryogenic temperatures. We suggest that the observed effects are due to the large inhomogeneous broadening of the excitonic PL and absorption bands resulting from the (PEA)2PbI4 band gap energy dependence on the number of lead(II) halide layers of individual crystallites. The characteristic time of the exciton energy funneling from higher- to lower-energy crystallites within (PEA)2PbI4 polycrystalline thin films is about 100 ps.

Synthesis of phenylethylammonium iodide (PEAI). 10 mL of phenylethylamine was added in a round bottom flask (100 mL) and then cooled down in an ice bath for 10 min. After that, 10 mL of HI (55% wt aqueous solution) was dropped very slowly. The reaction mixture was vigorously stirred approximately 60 min until a white solid precipitate. The solid was filtered and washed twice with cold diethyl ether. The solid was dried at 70 °C in a vacuum oven for 12 h.
Fabrication of polycrystalline thin films. The substrates (borosilicate glass) were exposed to UV-O 3 during 10 min. A compact layer of TiO 2 was deposited on the substrates by spray pyrolysis of titanium diisopropoxide bis(acac) solution (75% in 2-propanol, Sigma-Aldrich) diluted with absolute ethanol in 1:9 v/v proportion, respectively. The (PEA) 2 PbI 4 films were fabricated by modified hot casting method with 1:2 PbI 2 (0.1136 g) to PEAI (0.1227 g) molar ratio, 1 mL of DMF and 0.095 mL of DMSO. The perovskite precursor solution (50 μL), which was heated at 70 °C during all the process, was dripped on the substrate and spin coated at 4000 rpm during 20 s.
Finally, the samples were annealed at 100 °C during 10 min. The resulting film thickness was about 250-300 nm.
Fabrication of monocrystalline films. Such high-quality ultra-thin films were prepared in two steps following the procedure described in literature [1]. First, (PEA) 2 PbI 4 crystals are synthesized performing a liquid-liquid extraction of 9 mL of hydriodic acid (57% w/w in water, unstabilized, length grating spectrograph/spectrometer (1200 g/mm with 750 nm blaze) and detected by a Si micro photon device (MPD) and single-photon avalanche diode (SPAD) photodetector (connected through a multimode optical fiber to the monochromator); the SPAD was attached to a time correlated single photon counting electronic board (TCC900 from Edinburgh Instruments). The instrument response function is about 50 ps. For absorption spectra measurements, a xenon lamp was used.

Ab initio calculations.
The ab initio calculations of the optical spectra of (C 6 H 5 C 2 H 4 NH 3 ) 2 PbI 4 perosvkite have been performed using many-body perturbation theory as implemented in the Yambo code [2]. We have worked in the framework of the GW method and the Bethe-Salpeter Equation (BSE). In order to obtain the excitonic states and the optical spectra using BSE, we have calculated the eigenvalues and eigenvectors of the system using density-functional theory (DFT) within the local-density approximation (LDA) as implemented in Quantum Espresso [3]. We have used norm-conserving pseudopotentials, with a basis-set cutoff energy of 90 Ry and a sampling of the Brillouin zone with a 10x10x1 k-grid. In the case of the BSE calculations, we have used a 30x30x1 k-grid, 100 bands for the calculation of the static dielectric screening and the Coulomb cutoff to avoid artificial interaction between replicas of the supercell (see also Fig. S1 for explanation). Note that only spectral position of the excitonic transition was calculated, whereas the Lorentz contour with FWHM of 12 meV was used to present the absorption band in Fig. 2d.  Figure S1. Lateral and top view of the PEA 2 PbI 4 perovskite used in the simulations. The organic molecule is substituted by a cation atom for improving calculation efficiency. Cation atoms are shown as large green balls, Pb atoms as medium-sized purple balls, and I atoms as small purple balls.

Note 1. Determination of size of crystallites on the basis of the XRD lines broadening.
With use of Scherrer formula (S1), crystallite sizes D are determined for 5 XRD lines (Table S1).
(S1) = where D is a crystallite size, K is the Scherrer constant (0.9), λ is the X-ray source wavelength (0.154406 nm), β is the FWHM (radians), θ is the peak position (radians) On the basis of the data presented we conclude that the crystallite sizes are between 60 and 120 nm.   intensity I on temperature T is considered to be described by the formula = 0 [1 + • exp (where I 0 is the initial (unquenched) PL intensity, a is a constant, k is Boltzmann constant, E a is )] Arrhenius activation energy. Linearization of I(T) dependence is realized in the coordinates